Duke TIP; this was an introduction to programming in Matlab, with applications to fractals,
self-similarity, chaos and difference equations, etc. For example, students could
generate their own Koch-snowflake like fractals using Logo-like instructions around a skeleton code I wrote in Matlab.

Girls Talk Math; here I wrote a module going
in depth about the Mandelbrot set,
and guiding them to write their own code from scratch in Mathematica to visualize it.

I'm happy to discuss or share materials from most of these courses; feel free to send me an email.

Gallery

This is a collection of some of the images
and interactive visualizations I've produced as a
part of my teaching.

Portion of the Mandebrot fractal. Brightness corresponds
to number of iterations before escape, with a cutoff.
Students could go through worksheets towards building the
algorithm themself, or just modify parameters, colormap, etc
of a finished product. (Used in Duke TIP and Girls Talk Math)

Iterative generation of a Koch snowflake using
recursive "turtle"-style graphics. These are instructions
such as "go forward 2 units," "turn left 30 degrees,"
"turn right 45 degrees," etc. (Used in Duke TIP)

Visualization of the action of matrices in two dimensions.
The first figure illustrates the concept of singular value decomposition
(rotate, scale, rotate) by coloring the points in the domain by
their initial angle. The second figure shows the geometric
interpretation of the matrix 2-norm as the length of the semimajor axis
of the map of the unit ball. The matrix condition number is
the product of these semimajor axes under the forward map Ax
and the inverse map A-1x. (Used in Numerical Analysis)

Blood-Alcohol content model, where the value
follows an exponential decay law (alcohol decays with a
half-life in the model). The students
could specify what kind of drink(s) to have, and when,
by modifying an Excel file and seeing the resulting
graph. (Used in Introduction to Mathematical Modeling; for
non-math majors)

Visualization of Newton's method for finding
the root of a function, where arrows
follow the tangent line to its zero, then back to the
function at that value, visualized similar to a
cobweb plot.
The user can modify the function, intial guess, and number of
iterations. Useful for seeing when things go right, and
peculiar functions where things go very wrong.
(Used in Calculus 1; Numerical Analysis)

Visualization of a two-dimensional Riemann sum.
Included capability to change number of rectangles on the fly
to demonstrate convergence to the double integral.
(Used in Calculus 3)

Demonstration of a parameterized surface
(u(θ,φ), v(θ,φ), w(θ,φ)),
where fixed θ correspond to parameterized ellipses,
and fixed φ correspond to helices. Sliders in the
demonstration change the values of θ and φ and
highlight the corresponding portions of the surface (Used in Calculus 3)